Scale-free Network Model Research Articles

Research on invulnerability of the random scale-free network against cascading failure

The effect of structure parameters of random scale-free network on the network invulnerability for cascading failure is investigated by establishing a cascading failure model of random scale-free network based on node degree and analyzing the effect of node capacity on the cascading failure. The node capacity threshold is thus obtained. Furthermore, the relationship between the threshold of node capacity and the structure parameters of the network (the number of added edges per time slot and the power exponent) is established. The experimental results show that the structure parameters of the network are positively correlated with the network invulnerability for cascading failure. The more the number of added edges at a time and higher the power exponent, the stronger the network invulnerability for cascading failure.

Fast sparsely synchronized brain rhythms in a scale-free neural network

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D. For small D, full synchronization with the same population-rhythm frequency fp and mean firing rate (MFR) fi of individual neurons occurs, while for large D partial synchronization with fp>〈fi〉 (〈fi〉: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of fp>4〈fi〉 is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As D passes a critical value D* (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For D<D*, population synchronization emerges in the whole population because the spatial correlation length between the neuronal pairs covers the whole system. Furthermore, the degree of population synchronization is also measured in terms of two types of realistic statistical-mechanical measures. Only for the partial and sparse synchronization do contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike in the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of statistically homogeneous random graphs and small-world networks. Finally, we investigate the effect of network architecture on sparse synchronization for fixed values of J and D in the following three cases: (1) variation in the degree of symmetric attachment, (2) asymmetric preferential attachment of new nodes with different in- and out-degrees, and (3) preferential attachment between pre-existing nodes (without addition of new nodes). In these three cases, both relation between network topology (e.g., average path length and betweenness centralization) and sparse synchronization and contributions of individual dynamics to the sparse synchronization are discussed.

A Model for Scale-Free Networks: Application to Twitter

In the last few years, complex networks have become an increasingly relevant research topic due to the large number of fields of application. Particularly, complex networks are especially significant in the area of modern online social networks (OSNs). OSNs are actually a challenge for complex network analysis, as they present some characteristics that hinder topology processing. Concretely, social networks’ volume is exceedingly big, as they have a high number of nodes and links. One of the most popular and influential OSNs is Twitter. In this paper, we present a model to describe the growth of scale-free networks. This model is applied to Twitter after checking that it can be considered a “scale-free” complex network fulfilling the small world property. Checking this property involves the calculation of the shortest path between any two nodes of the network. Given the difficulty of this computation for large networks, a new heuristic method is also proposed to find the upper bounds of the path lengths instead of computing the exact length.

Ashkin-Teller model and diverse opinion phase transitions on multiplex networks.

Multiplex networks (MNs) have become a platform of recent research in network sciences because networks in many real-world systems interact and function together. One of the main scientific issues in MNs is how the interdependence changes the emerging patterns or phase transitions. Until now, studies of such an issue have concentrated on cluster-breakdown phenomena, aiming to understand the resilience of the system under random failures of edges. These studies have revealed that various phase transition (PT) types emerge in MNs. However, such studies are rather limited to percolation-related problems, i.e., the limit q→1 of the q-state Potts model. Thus, a systematic study of opinion formation in social networks with the effect of interdependence between different social communities, which may be seen as the study of the emerging pattern of the Ising model on MNs, is needed. Here we study a well-known spin model called the Ashkin-Teller (AT) model in scale-free networks. The AT model can be regarded as a model for interacting systems between two species of Ising spins placed on respective layers in double-layer networks. Our study shows that, depending on the interlayer coupling strength and a network topology, unconventional PT patterns can also emerge in interaction-based phenomena: continuous, discontinuous, successive, and mixed-order PTs and a continuous PT not satisfying the scaling relation. The origins of such rich PT patterns are elucidated in the framework of Landau-Ginzburg theory.

Synchronization in scale-free networks: The role of finite-size effects

Synchronization problems in complex networks are very often studied by researchers due to their many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, scale-free networks with degree distribution , are widely used in research since they are ubiquitous in Nature and other real systems. In this paper we focus on the surface relaxation growth model in scale-free networks with , and study the scaling behavior of the fluctuations, in the steady state, with the system size N. We find a novel behavior of the fluctuations characterized by a crossover between two regimes at a value of that depends on λ: a logarithmic regime, found in previous research, and a constant regime. We propose a function that describes this crossover, which is in very good agreement with the simulations. We also find that, for a system size above , the fluctuations decrease with λ, which means that the synchronization of the system improves as λ increases. We explain this crossover analyzing the role of the network's heterogeneity produced by the system size N and the exponent of the degree distribution.

Ising model in clustered scale-free networks.

The Ising model in clustered scale-free networks has been studied by Monte Carlo simulations. These networks are characterized by a degree distribution of the form P(k)∼k(-γ) for large k. Clustering is introduced in the networks by inserting triangles, i.e., triads of connected nodes. The transition from a ferromagnetic (FM) to a paramagnetic (PM) phase has been studied as a function of the exponent γ and the triangle density. For γ>3 our results are in line with earlier simulations, and a phase transition appears at a temperature T(c)(γ) in the thermodynamic limit (system size N→∞). For γ≤3, a FM-PM crossover appears at a size-dependent temperature T(co), so the system remains in a FM state at any finite temperature in the limit N→∞. Thus, for γ=3, T(co) scales as lnN, whereas for γ<3, we find T(co)∼JN(z), where the exponent z decreases for increasing γ. Adding motifs (triangles in our case) to the networks causes an increase in the transition (or crossover) temperature for exponent γ>3 (or ≤3). For γ>3, this increase is due to changes in the mean values 〈k〉 and 〈k(2)〉, i.e., the transition is controlled by the degree distribution (nearest-neighbor connectivities). For γ≤3, however, we find that clustered and unclustered networks with the same size and distribution P(k) have different crossover temperature, i.e., clustering favors FM correlations, thus increasing the temperature T(co). The effect of a degree cutoff k(cut) on the asymptotic behavior of T(co) is discussed.

A random geometric graph built on a time-varying Riemannian manifold

The theory of random geometric graph enables the study of complex networks through geometry. To analyze evolutionary networks, time-varying geometries are needed. Solutions of the generalized hyperbolic geometric flow are such geometries. Here we propose a scale-free network model, which is a random geometric graph on a two dimensional disc. The metric of the disc is a Ricci flat solution of the flow. The model is used to physically simulate the growth and aggregation of a type of cancer cell.

Energy-saving Strategy Based on an Immunization Algorithm for Network Traffic

The rapid development of both communication traffic and increasing optical network sizes has increased energy consumption. Traditional algorithms and strategies don’t apply to controlling the expanded network. Immunization algorithms originated from the complex system theory are feasible for large-scale systems based on a scale-free network model. This paper proposes the immunization strategy for complex systems which includes random and targeted immunizations to solve energy consumption issues and uses traffic to judge the energy savings from the node immunization. The simulation results verify the effectiveness of the proposed strategy. Furthermore, this paper provides a possibility for saving energy with optical transmission networks.

Exactly scale-free scale-free networks

Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to model the growth and structure of scale-free networks. With so many different models of scale-free networks it is unclear what properties of scale-free networks are typical, and what properties are peculiarities of a particular growth or construction process. We propose a simple maximum entropy process which provides the best representation of what are typical properties of scale-free networks, and provides a standard against which real and algorithmically generated networks can be compared. As an example we consider preferential attachment and find that this particular growth model does not yield typical realizations of scale-free networks. In particular, the widely discussed “fragility” of scale-free networks is actually found to be due to the peculiar “hub-centric” structure of preferential attachment networks. We provide a method to generate or remove this latent hub-centric bias—thereby demonstrating exactly which features of preferential attachment networks are atypical of the broader class of scale-free networks. We are also able to statistically demonstrate whether real networks are typical realizations of scale-free networks, or networks with that particular degree distribution; using a new surrogate generation method for complex networks, exactly analogous the widely used surrogate tests of nonlinear time series analysis.

Growing optimal scale-free networks via likelihood.

Preferential attachment, by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree, has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree k is proportional to k^{-γ}. However, the motivation for this model is entirely ad hoc. We use exact likelihood arguments and show that the optimal way to build a scale-free network is to attach most new links to nodes of low degree. Curiously, this leads to a scale-free network with a single dominant hub: a starlike structure we call a superstar network. Asymptotically, the optimal strategy is to attach each new node to one of the nodes of degree k with probability proportional to 1/N+ζ(γ)(k+1)(γ) (in a N node network): a stronger bias toward high degree nodes than exhibited by standard preferential attachment. Our algorithm generates optimally scale-free networks (the superstar networks) as well as randomly sampling the space of all scale-free networks with a given degree exponent γ. We generate viable realization with finite N for 1≪γ<2 as well as γ>2. We observe an apparently discontinuous transition at γ≈2 between so-called superstar networks and more treelike realizations. Gradually increasing γ further leads to reemergence of a superstar hub. To quantify these structural features, we derive a new analytic expression for the expected degree exponent of a pure preferential attachment process and introduce alternative measures of network entropy. Our approach is generic and can also be applied to an arbitrary degree distribution.

Forest-fire model as a supercritical dynamic model in financial systems.

Recently large-scale cascading failures in complex systems have garnered substantial attention. Such extreme events have been treated as an integral part of self-organized criticality (SOC). Recent empirical work has suggested that some extreme events systematically deviate from the SOC paradigm, requiring a different theoretical framework. We shed additional theoretical light on this possibility by studying financial crisis. We build our model of financial crisis on the well-known forest fire model in scale-free networks. Our analysis shows a nontrivial scaling feature indicating supercritical behavior, which is independent of system size. Extreme events in the supercritical state result from bursting of a fat bubble, seeds of which are sown by a protracted period of a benign financial environment with few shocks. Our findings suggest that policymakers can control the magnitude of financial meltdowns by keeping the economy operating within reasonable duration of a benign environment.

Effects of Cluster Network Structure to the Behavior of Enterprise Imitation

Since the 1990s, the research of cluster economy gradually becomes a topic of interest for academic econo- mists and Management experts. In order to obtain the effects of cluster network structure on the behavior of enterprise im- itation, based on neighbor effect, this paper builds dynamic model of a single enterprise income, then explores the propa- gation of corporate behavior under random network model, small world network model, scale-free network model. On the basis of neighbor average profit, this article makes a comparative analysis of the network structure imitation and then ar- rives at the cluster network structure's influence on the enterprise imitation.

A Complex Network Approach to Topology Control Problem in Underwater Acoustic Sensor Networks

Underwater acoustic sensor networks (UASNs) have been developed for a set of underwater applications, including resource exploration, pollution monitoring, and tactical surveillance. Topology control techniques of UASNs are significantly different from those of terrestrial wireless sensor networks, due to the properties of underwater environments and acoustic communications. This research begins with a scale-free network model for calculating edge probability, which is used to generate initial topology randomly. Subsequently, a topology control strategy based on complex network theory (TCSCN) is put forward to construct a double clustering structure, where there are two kinds of cluster-heads to ensure connectivity and coverage, respectively. The performance of TCSCN is analyzed through simulation experiments that indicate a well-constructed topology, where (1, $\xi$ )-Coverage and (1, $\zeta$ )-Connectivity can be achieved while optimizing energy consumption and propagation delay as much as possible.

Node influence identification via resource allocation dynamics

Identifying the node influence in complex networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the resource allocation dynamics (RAD) and the k-shell decomposition method, we present an improved method namely RAD to generate the ranking list to evaluate the node influence. First, comparing with the epidemic process results for four real networks, the RAD method could identify the node influence more accurate than the ones generated by the topology-based measures including the degree, k-shell, closeness and the betweenness. Then, a growing scale-free network model with tunable assortative coefficient is introduced to analyze the effect of the assortative coefficient on the accuracy of the RAD method. Finally, the positive correlation is found between the RAD method and the k-shell values which display an exponential form. This work would be helpful for deeply understanding the node influence of a network.

Analyses of Complex Networks Based on the Random Walk Model

In this letter, we derive the analytical expressions of the degree distributions for a kind of networks model random initializing attractiveness and preferential linking, which analyzed degree evolution by using the master equation approach. We also discuss the theoretical justification of the scale-free behavior about the proposed model. The influencing range of initialization to the degree distribution only related to initialization’s expectation under the global meaning. Finally, a series of theoretical analysis and numerical simulations to the scale-free network model are conducted in this letter. The results of computer simulation is presented to the theoretical analysis.

A two-step high-risk immunization based on high-risk immunization.

In this paper, the two-step high-risk immunization was investigated based on high-risk immunization for the SIRS model in small-world networks and scale-free networks. First, the effects of various immunization schemes are studied and compared. When the number of immune is same, the research result shows that the immune effect of the two-step high-risk immunization strategy is not the best nor the worst. However, the practicability is better compare with others. Furthermore, by changing the proportional of immunization the optimal immune effect can be achieved in the two-step high-risk immunization. Computation results verify that the two-step high-risk immunization is effective, and it is economic and feasible in practice.

Quantum Google algorithm

We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks. The algorithm has been shown to identify unambiguously the underlying topology of the network and to be capable of clearly highlighting the structure of secondary hubs of networks. Furthermore, it can resolve the degeneracy in importance of the low-lying part of the list of rankings. Examples of applications include real-world instances from the WWW, which typically display a scale-free network structure and models of hierarchical networks. The quantum algorithm has been shown to display an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance among the nodes, as compared to the classical algorithm.

Random Immunization Algorithm to Energy Consumption in Optical Network

The immunization algorithm is from the theory of complex network. The algorithm is simple, highly feasible based on scale-free network model. This paper uses random immunization algorithm to solve optical network energy issues. This paper selects the service to be the operator and to save energy through node immunization. The simulation results show the algorithm can be implemented. This paper provides another possibility to energy saving on optical network.

Scale‐free network model for template matching based on kernel histogram

A novel method to build a scale-free network model for template matching is proposed. The scale-free network model of the template is produced by a kernel histogram. Moreover, those special points that have much larger effects than other points can be selected by a matching algorithm. Based on the scale-free network model, the matching is implemented by minimising the sum of absolute differences. The proposed algorithm can match the potential object of varying scale in a clutter background. To the best of the authors' knowledge, this is the first template matching algorithm which uses the scale-free complex network to model template matching.

General and craniofacial development are complex adaptive processes influenced by diversity

Complex systems are present in such diverse areas as social systems, economies, ecosystems and biology and, therefore, are highly relevant to dental research, education and practice. A Complex Adaptive System in biological development is a dynamic process in which, from interacting components at a lower level, higher level phenomena and structures emerge. Diversity makes substantial contributions to the performance of complex adaptive systems. It enhances the robustness of the process, allowing multiple responses to external stimuli as well as internal changes. From diversity comes variation in outcome and the possibility of major change; outliers in the distribution enhance the tipping points. The development of the dentition is a valuable, accessible model with extensive and reliable databases for investigating the role of complex adaptive systems in craniofacial and general development. The general characteristics of such systems are seen during tooth development: self-organization; bottom-up emergence; multitasking; self-adaptation; variation; tipping points; critical phases; and robustness. Dental findings are compatible with the Random Network Model, the Threshold Model and also with the Scale Free Network Model which has a Power Law distribution. In addition, dental development shows the characteristics of Modularity and Clustering to form Hierarchical Networks. The interactions between the genes (nodes) demonstrate Small World phenomena, Subgraph Motifs and Gene Regulatory Networks. Genetic mechanisms are involved in the creation and evolution of variation during development. The genetic factors interact with epigenetic and environmental factors at the molecular level and form complex networks within the cells. From these interactions emerge the higher level tissues, tooth germs and mineralized teeth. Approaching development in this way allows investigation of why there can be variations in phenotypes from identical genotypes; the phenotype is the outcome of perturbations in the cellular systems and networks, as well as of the genotype. Understanding and applying complexity theory will bring about substantial advances not only in dental research and education but also in the organization and delivery of oral health care.